With the proliferation of internet applications, it is expected that the mobile traffic volume supported by communication networks by 2020 will be almost 500 times larger than that supported today. To respond favourably to such constraints while keeping a high level of user quality of experience, system capacity and user fairness should be largely improved for the future 5th generation (5G) mobile communication systems. To this end, Non-Orthogonal Multiple Access (NOMA) has recently emerged as a promising candidate for future radio access. By exploiting an additional multiplexing domain, the power domain, NOMA allows the cohabitation of multiple users per sub-band at the transmitter side, on top of the Orthogonal Frequency Division Multiplexing (OFDM) layer, and relies on Successive Interference Cancellation (SIC) at the receiver side. An attractive feature of NOMA is that it targets the improvement of system capacity while achieving user fairness. Therefore, most of the prior art dealing with NOMA considers the proportional fairness (PF) scheduler as a multiuser scheduling scheme for the trade-off between total user throughput and the user fairness that it provides. Several power allocation algorithms, jointly implemented with a NOMA-based PF scheduler, have been proposed in recent research literature.
In “Uplink non-orthogonal access with MMSE-SIC in the presence of inter-cell interference” by Y. Endo, Y. Kishiyama, and K. Higuchi, in proc. 2012 IEEE Int. Symp. on Wireless Commun. Syst. 2012, an inter-cell interference-aware transmission and power control mechanism is proposed and conducted in two steps, followed by user selection based on the PF metric. In the first step, the transmission power of a user per sub-band is determined by the fractional transmit power control (FTPC) used in LTE. The power is then updated in a second step by taking into consideration the candidate set of scheduled users. Simulation results show that NOMA combined with the proposed power allocation greatly enhances the system-level throughput, compared to orthogonal access.
In “System-Level Performance of Downlink Non-orthogonal Multiple Access (NOMA) Under Various Environments” by Y. Saito, A. Benjebbour, Y. Kishiyama, and T. Nakamura in proc. IEEE 81st VTC, 2015, the system level-performance of downlink NOMA in small cells is investigated, where the full search power allocation scheme in “System-Level Performance of Downlink NOMA Combined with SUMIMO for Future LTE Enhancements”, by A. Benjebbour, A. Li, Y. Kishiyama, H. Jiang, and T. Nakamura, in proc. IEEE Globecom, December 2014 is conducted within the PF scheduler, in order to select the best combination of user pairs and power allocations. Some of the recently proposed power allocation algorithms for NOMA do not consider an equal inter-sub-band power distribution, while others propose different multi-user power allocation schemes with an equal distribution of power among sub-bands.
In “System-level performance evaluation of downlink non-orthogonal multiple access (NOMA)”, by Y. Saito, A. Benjebbour, Y. Kishiyama, and T. Nakamura, in proc. IEEE PIMRC, September 2013, and “A Concept and practical considerations of non-orthogonal multiple access (NOMA) for future radio access”, by. Benjebbour, Y. Saito, Y. Kishiyama, A. Li, A. Harada, A, and T. Nakamura, in proc. Int. Symp. on Intelligent Signal Process. and Commun. Syst. (ISPACS), 2013, the fractional transmit power allocation (FTPA) is introduced in order to split power among multiplexed users, while power per sub-band is considered to be constant over all frequency blocks. In “Performance of non-orthogonal access with SIC in cellular downlink using proportional fair-based resource allocation”, N. Otao, Y. Kishiyama, and K. Higuchi, in proc. Int. Symp. on Wireless Commun. Syst., 2012, pp. 476-480., power is also maintained constant for all sub-bands, but an optimal power allocation method based on iterative waterfilling is used to allocate power among scheduled users on each sub-band.
If a downlink system with single transmitter and receiver antenna is considered, the system consists of K users per cell, with a total system bandwidth B divided into S sub-bands, and a maximum allowable transmit power Pmax by the Base Station. Among the K users, a set of users Us={k1, k2, . . . , kn, . . . , kn(s)}, is selected to be scheduled over each frequency sub-band s, (1≤s≤S). n(s) indicates the number of users non-orthogonally scheduled at sub-band s. The SIC process as described in Fundamentals of Wireless Communication, Cambridge University Press, 2005 by D. Tse, and P. Viswanath, is conducted at the receiver side, and the optimum order for user decoding is in the increasing order of the users' channel gains normalized by the noise and inter-cell interference
      h          s      ,              k        n              2        n          s      ,              k        n            where hs,kn2 is the equivalent channel gain, at sub-band s, between user kn and the BS, and ns,kn the average power of the received Gaussian noise plus intercell interference by user kn. Assuming successful decoding and no SIC error propagation, and supposing that inter-cell interference is randomized such that it can be considered as white noise, the throughput of user kn, at sub-band s, Rs,kn, is given by:
                              R                      s            ,                          k              n                                      =                              B            S                    ⁢                                    log              2                        (                          1              +                                                                    h                                          s                      ,                                              k                        n                                                              2                                    ⁢                                      P                                          s                      ,                                              k                        n                                                                                                                                                        ∑                                                                        j                          ∈                                                      N                            s                                                                          ,                                                                                                            h                                                              s                                ,                                                                  k                                  n                                                                                            2                                                                                      n                                                              s                                ,                                                                  k                                  n                                                                                                                                              <                                                ,                                                                              h                                                          s                              ,                                                              k                                j                                                                                      2                                                                                n                                                          s                              ,                                                              k                                nj                                                                                                                                                                          ⁢                                                                  h                                                  s                          ,                                                      k                            n                                                                          2                                            ⁢                                              P                                                  s                          ,                                                      k                            j                                                                                                                                +                                      n                                          s                      ,                                              k                        n                                                                                                                  )                                              (        1        )            
The transmit power allocation constraint is represented by
                                                        ∑                              s                =                1                            S                        ⁢                                                  ⁢                          P              s                                =                      P            max                          ,                              with            ⁢                                                  ⁢                          P              s                                =                                    ∑                              n                =                1                                            n                ⁡                                  (                  s                  )                                                      ⁢                                                  ⁢                          P                              s                ,                                  k                  n                                                                                        (        2        )            
Where Ps denotes the amount of allocated power on sub-band s.
Since the scheduler in NOMA may allocate a sub-band to more than one user simultaneously, the user scheduling policy and the power allocation algorithm largely affect system efficiency and user fairness. A “Proportional Fairness” (PF) scheduler is known to achieve a good trade-off between these two metrics.
The objective of the PF scheduler is to maximize the logarithmic sum of user throughputs or, equivalently, long term averaged user rates, in order to ensure balance between cell throughput and user fairness. This scheduling policy has been adopted in the majority of proposed NOMA implementations. The scheduling algorithm keeps track of the average throughput Tk(t) of each user in a past window of length tc, where tc defines the throughput averaging time window (number of simulated subframes). Tk(t) is defined as:
                                          T            k                    ⁡                      (                          t              +              1                        )                          =                                            (                              1                -                                  1                                      t                    c                                                              )                        ⁢                                          T                k                            ⁡                              (                t                )                                              +                                    1                              t                c                                      ⁢                                          ∑                                  s                  =                  1                                S                            ⁢                                                          ⁢                                                R                                      s                    ,                    k                                                  ⁡                                  (                  t                  )                                                                                        (        3        )            
where Rs,k(t) represents the throughput of user k on sub-bands, at time instance t. This is calculated based on Eq. (1) above, and can equal zero if user k is not scheduled on sub-band s.
For each sub-band s, all possible candidate user sets are considered, and the set of scheduled users Us is chosen in such a way to maximize the PF scheduling metric:
                              U          s                =                              argmax            U                    ⁢                                    ∑                              k                ∈                U                                      ⁢                                                  ⁢                                                            R                                      s                    ,                                          k                      |                      U                                                                      ⁡                                  (                  t                  )                                                                              T                  k                                ⁡                                  (                  t                  )                                                                                        (        4        )            
A difficulty with this approach is that power allocation on the basis for example of the Proportional Fairness calculation depends on knowledge of user throughput on a specified sub-band, which implies that users have already been allocated to particular sub-bands. Meanwhile, in NOMA systems, maximum throughput can generally be achieved where there is the greatest possible difference in transmission power for the users on a given sub-band, so that optimal allocation of users to sub-bands requires knowledge of the power available for each user. Accordingly, the considerations are mutually interdependent. It is desirable to identify a mechanism for resolving this tension and providing a method for a more optimal attribution of sub-bands and data rates resulting in improved overall data throughput.